Here \(\rho _{f;a}\)  is the resistivity of \(f_{a}\)  in the layer \(a\) . \(\sigma _b\)  is the conductivity for the slave boson \(\varphi \)  at the critical point. Then we can see that \(\rho _{11}=\rho _{f;t}+\rho _b\)  has contributions from both fermion and critical boson as in single layer case[1]}. However, \(\rho _{12}=\rho _b\)  is dominated by the resistivity of the slave boson now. Because the boson \(\varphi \)  goes through a superfluid-insulator transition, we expect that the drag resistivity \(\rho _{12}\)  shows similar behavior as the resistivity across a superconductor-insulator transition, as illustrated in Fig. REF . Especially there is a large drag resistivity \(R_0=\frac{1}{\sigma _b^c}\)  at order \(\frac{h}{e^2}\)  in the critical regime. Around the critical point, we also anticipate a scaling in the form \(\rho (T,x-x_c)= a F(\frac{T}{|x-x_c|^{\nu z}})\)  with \(\nu z \approx 0.67\) . Such a scaling has been seen in experiment for the MoTe\(_2\) /Wse\(_2\)  system[2]}. It is interesting to test the scaling also in the moire+monolayer system tuned by exciton density.
